Intentionally allowing or promoting invasion by non‐native trees into areas characterized by treeless vegetation could contribute to climate‐change mitigation by increasing carbon (C) sequestration. In some areas of the world, incentives exist to retain invasive non‐native trees in natural systems as a mechanism for increasing ecosystem C storage and reducing atmospheric carbon dioxide levels. Although this novel opportunity for C sequestration holds appeal, such an approach is problematic for several reasons: (1) invasive trees do not always increase net C sequestration due to greater occurrence of fire or reduced soil C; (2) lower albedo in invaded areas can increase absorption of solar radiation, thereby offsetting potential C sequestration; and (3) tree invasions often also have negative effects on biodiversity, economic opportunities, and water yield. Such drawbacks are sufficient to raise doubts about the widespread use of non‐native tree invasions in treeless areas as a tool to ameliorate climate change.